DMCA
A Continuum Approximation for the Excitations of the (1, 1, ..., 1) Interface in the Quantum Heisenberg model (1999)
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BibTeX
@MISC{Bolina99acontinuum,
author = {Oscar Bolina and Pierluigi Contucci and Bruno Nachtergaele and Shannon Starr},
title = {A Continuum Approximation for the Excitations of the (1, 1, ..., 1) Interface in the Quantum Heisenberg model},
year = {1999}
}
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Abstract
: It is shown that, with an appropriate scaling, the energy of lowlying excitations of the (1; 1; : : : ; 1) interface in the d-dimensional quantum Heisenberg model are given by the spectrum of the d \Gamma 1-dimensional Laplacian on an suitable domain. Keywords: Anisotropic Heisenberg ferromagnet, XXZ model, interface excitations, 111 interface. MCS2000 numbers: 82B10, 82B24, 82D40 Copyright c fl 1999 Bolina, Contucci, Nachtergaele, and Starr. Reproduction of this article in its entirety, by any means, is permitted for non-commercial purposes. 2 1 Introduction and main results We consider the spin 1/2 XXZ Heisenberg model on the d-dimensional lattice Z d . For any finite volume ae Z d , the Hamiltonian is given by H = \Gamma X x;y2 jx\Gammayj=1 \Delta \Gamma1 (S (1) x S (1) y + S (2) x S (2) y ) + S (3) x S (3) y ; (1.1) where \Delta ? 1 is the anisotropy. We refer to the next section for more precise definitions. By adding an appropriate boundary term o...
Keyphrases
continuum approximation quantum heisenberg model finite volume ae d-dimensional quantum heisenberg model d-dimensional lattice xxz model mcs2000 number non-commercial purpose anisotropic heisenberg ferromagnet appropriate boundary term gamma 1-dimensional laplacian main result jx gammayj precise definition delta gamma1 appropriate scaling suitable domain interface excitation next section xxz heisenberg model
